Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves

Abstract

In this paper, we will obtain new algebraic transformations of the ${}_2{F}_1$-hypergeometric functions. The main novelty in our approach is the interpretation of identities among ${}_2{F}_1$-hypergeometric functions as identities among automorphic forms on different Shimura curves.

31 pages

References in corpus (1)

• Schwarzian differential equations and Hecke eigenforms on Shimura curves